macbook air black screen, chime and logo on boot

Make an appointment at the Apple Genius Bar for service. If you need to find an Apple Store - Find a Store - Apple.

You might try, if you haven't already, these 2-things that might help:

1. First, reboot the computer, using the power button, WHILE HOLDING DOWN THE SHIFT KEY until you hear the 'bong'.

2. If that doesn't work, reboot as above, WHILE HOLDING DOWN COMMAND-R until you hear the 'bong'.

Hints:

1. Don't rush the reboot-hold down the power button for a while AFTER everything has died- then release the power button for a moment-then hold the power button down again while trying the above sequences.

2. Go back and forth between the 2-sequences above. In my case, one or the other eventually works, but when it really gets stubborn a shutdown for an hour or so improves the odds (cooling off?).

3. The above technique may be pertinent to a specific computer ( mine is a desktop - iMac ), but the technique has been touted on the web for years. GOOD LUCK.